We describe isotropic orbits for the restricted action of a subgroup of a Lie group acting on a symplectic manifold by Hamiltonian symplectomorphisms and admitting an Ad*-equivariant moment map. We obtain examples of Lagrangian orbits of complex flag manifolds, of cotangent bundles of orthogonal Lie groups, and of products of flags. We introduce the notion of infinitesimally tight and study the intersection theory of such Lagrangian orbits, giving many examples.

中文翻译：

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无限紧拉格朗日轨道

我们通过哈密顿辛同胚描述了李群的一个子群的限制作用的各向同性轨道，该子群通过哈密顿辛同胚作用在辛流形上并允许一个 Ad* 等变矩图。我们获得了复旗流形的拉格朗日轨道、正交李群的余切丛和旗的乘积的例子。我们引入了无穷小紧的概念并研究了这种拉格朗日轨道的相交理论，给出了许多例子。